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dc.contributor.authorReynes, Josephine Elizabeth Anne ( )
dc.date.accessioned2020-06-17T15:55:08Z
dc.date.available2020-06-17T15:55:08Z
dc.date.issued2019-05
dc.identifier.citationReynes, J. (2019). Total minor polynomials of oriented hypergraphs (Unpublished thesis). Texas State University, San Marcos, Texas.
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/11844
dc.descriptionPresented to the Honors Committee of Texas State University in Partial Fulfillment of the Requirements for Graduation in the University Honors Program, May 2019.
dc.description.abstractConcepts of graph theory can be generalized to integer matrices through the use of oriented hypergraphs. An oriented hypergraph is an incidence structure consisting of vertices, edges, and incidences, equipped with three functions: a vertex incidence function, an edge incidence function, and an incidence orientation function. This thesis provides a unifying generalization of Seth Chaiken’s All-Minors Matrix-Tree Theorem and Sachs’ Coefficient Theorem to all integer adjacency and Laplacian matrices – extending the results of Rusnak, Robinson et. al. – by introducing a polynomial in |V|2 indeterminants indexed by minor order whose monomial coefficients are the minors. The coefficients are determined by embedding the oriented hypergraph into the smallest uniform hypergraph that contains it and summing over a class of sub-monic mappings of paths of length one relative to the original oriented hypergraph. It is known that the non-cancellative mappings associated to each degree-1 monomials are in one-to-one correspondence with Tuttes Matrix-Tree Theorem. This is extended to Tuttes k-arborescence decomposition via the degree-k monomials.en_US
dc.formatText
dc.format.extent35 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.subjectLaplacianen_US
dc.subjectHypergraphen_US
dc.subjectSigned graphen_US
dc.subjectCharacteristicen_US
dc.subjectPolynomialen_US
dc.subjectMatrix-tree theoremen_US
dc.subjectCombinationsen_US
dc.titleTotal Minor Polynomials of Oriented Hypergraphsen_US
txstate.documenttypeThesis
thesis.degree.departmentHonors College
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas State University
txstate.departmentHonors College


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